Dr. Tom Price, secretary of the Department of Health and Human Services, told ABC News this morning that it is "certainly the goal" for health care to be less expensive and to provide coverage for all, but he didn't guarantee that would be the case.

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Of the GOP's proposed Obamacare replacement, Price said he and his colleagues are trying to "fix a system that isn't working."

The new health care bill, which was previewed by House Republicans this week, bears some similarities to the Obama-era Affordable Care Act (ACA): tax credits, protections for people with health problems and the ability of parents to keep young adults on their insurance. It has nevertheless drawn sharp criticism from Democrats, health care advocates, and even many conservatives, who would prefer to see a total repeal.

"We're going to do something that's great and I'm proud to support the replacement plan released by the House of Representatives," Trump said at the White House Tuesday.

"We're going to take action. There's going to be no slowing down. There's going to be no waiting and no more excuses by anybody," he added.

Today, Price defended the bill from critics on both sides and attempted to paint it as step forward.

"The current system is not satisfactory," Price said of the Affordable Care Act, which has served as a lightning rod for criticism since Obama signed it into law in March of 2010.

When asked if the bill met Trump's stated goal of providing "insurance for everybody," Price dodged the issue, and turned the focus to costs, suggesting that premiums and deductibles are rising as a result of the ACA.

"The current system is not satisfactory for many individuals," Price said.

Trump told House Republicans on Tuesday that he would engage with individual lawmakers who oppose the new bill, The Associated Press reported.

Trump tweeted at one such member, Sen. Rand Paul of Kentucky, who voiced criticism of the bill. Trump wrote, "I feel sure that my friend @RandPaul will come along with the new and great health care program because he knows Obamacare is a disaster!"